Identify

Many furniture was designed harmful for children, many children were injured or killed due to tip over of the furniture. Dressers designed like this (fig. 1) has killed 7 children and got many injured. In 2016, IKEA recalled many dressers that have potential to tip over while kids climbing it. For a 8-year-old child, is it possible to tip the dresser over when climbing? Unknown: sum of the moment at the center of tip-over.

(fig. 1: dresser tip over due to defect)

(fig 2: information of one of the dressers IKEA recalled in 2016)

Formulate

Goal: find the moment at point O.

Formula to use: M = F*d(perpendicular)

The dresser is 134 cm tall, and 48 cm deep. Width is not necessary to measure since we are using a 2-d model.

First, we set up a 2D model to solve the problem (fig. 3).

O: point of tip-over. A: center of mass of the child. B: center of mass of the 3 drawers inserted. C: center of mass of the dresser (without drawers). D: center of mass of the top drawer that is out.

Drawers are 9.25 kg each. Dresser without drawer is 35.97 kg. Mass of a 8-years-old child: 23 kg. A(-55, 75), B(24,50), C(24,67), D(-24, 100)

Assumptions: the dresser is uniformed in weight. weight of the foots and top are negligible. No other things in the drawer. The top drawer is fully out and other drawers are fully inside. Center of mass occur at the geometric center of the main body.

(fig. 3 2-D model for the problem.)

Solve

ΣM= 28 kg* 9.8N/kg* -0.55m+3*9.25kg* 9.8N/kg* 0.24m+35.95kg* 9.8N/kg* 0.24m+9.25kg* 9.8N/kg* -0.24m = -150.92+65.27+84.56-21.76=-22.85N-m

The answer implies that a 8-year-old child is able to tip the dresser over by climbing on the top of the drawer. We assumed that the dresser is empty, and uniformed in weight. However, in real-life the problem could be more specific. Also we simplified the problem as a 2-D problem which implies that the dresser would only tip to the left, but in 3-D world the it could tip at any angle. Further, only one case which the child hangs one the top drawer with other drawers inserted was analyzed, but many other situation could happen in real-life.

The answer is reasonable since all values used were real-life values, and that is why the products were recalled.

In this case, any child weighs over 26 kg has potential to tip over the dresser and get injured or killed.

links:

http://abc7chicago.com/family/safety-group-highlights-recalls-of-childrens-products/1833068/

https://www.disabled-world.com/artman/publish/height-weight-teens.shtml

http://www.ikea.com/gb/en/products/storage-furniture/chest-of-drawers/brusali-chest-of-4-drawers-white-art-20252742/

http://www.ikea.com/ms/en_CA/pdf/Recalled_Chest_of_Drawers_Jun29_EN.pdf?icid=itl|ca|en_secureit_pdf|201606282141595720_1